My wife bought the note 3 tmobile month and a half ago and didn't have issues until recently when I updated nope so I sent it back in to get a new one and for some reason its having issues again and this is a new note 3 from T Mobile my phone cuts off it lags the connectivity goes off the 4G disappears the wifi disconnects is this a defective device that was sent to me and should T Mobile investigate these phones more. Also I hope that people on this forum is calling in to T Mobile on these issues so that we can have a better experience claim is an excellent phone.
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Re: defective device
Welcome to Android Central! If the same problems occur on the new phone compared with the old one, I'd wonder if something that you're installing is causing issues. You could try booting into Safe Mode, which disables all 3rd party apps, and see if the problems persist. If not, then something you installed is the culprit. If the problems do persist, then you're right, there's something wrong with either the hardware or the firmware.
You could also try booting into Recovery Mode and wiping the cache partition, which doesn't erase any personal data. Steps for this and for Safe Mode are here: Reset: Samsung Galaxy Note 3 | T-Mobile Support
Are problems only with calls and 4G connectivity? You mentioned wi-fi problems, too--are you certain of that? I'm trying to figure out if this might be a T-Mobile network issue rather than a phone issue.